Pricing in a semi-Markov modulated jump diffusion model

Abstract

In this thesis, we introduce a new market model for the stock price dynamics. It is a regime switching market where the parameters volatility and drift follows a semi-Markov process. In addition to that along with the diffusion process, we incorporate a term which give us the discontinuity in the market. We call this market model a semi-Markov modulated jump diffusion model. Apart from defining a market model by stochastic differential equation (SDE), we find the solution of this SDE. Then we derive the infinitesimal generator associated with this model so that some further investigations can be carried out. Finally we have shown that this model is arbitrage free.